Question

Solve the equation $x^5-5x^3+4x=0$.

Short answer

The solution for the equation is $x=0,-2,2,-1,1$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $x^5-5x^3+4x=0$.

Step 2. Simplify the equation.

The given equation $x^5-5x^3+4x=0$is solved as:

localid="1648547996373" $\begin{array}{c}{x}^5-5x^3+4x=0....\left(\text{Given}\right)\\ x\left(x^4-5x^2+4\right)=0\\ x=0\text{or}{x}^4-5x^2+4=0\\ x=0\text{or}\left(x^2-4\right)\left(x^2-1\right)=0\\ x=0\text{or}{x}^2-4=0\text{or}{x}^2-1=0\\ x=0\text{or}x=\pm 2\text{or}x=\pm 1\end{array}$

Step 3. Conclusion.

The solution for the given equation is $x=0,-2,2,-1,1$.